We demonstrate the existence of a special degeneracy condition, called degenerate band edge (DBE), between two Bloch modes in periodically-loaded circular all-metallic waveguides at microwave frequencies. The DBE condition has been associated with a dramatic reduction in group velocity and with some unique resonance properties, but it has not been shown in hollow waveguide structures yet. Hence, we show here its existence in two periodic waveguide examples. The unit cell of the first structure is composed of a circular waveguide loaded with two inner cylinders with elliptical irises with misaligned angles. The second structure is composed by loading the waveguide with elliptical rings. The demonstration of DBE in those waveguide is explained through a simple multi-transmission line approach where the conditions to obtain DBE are clarified, and suggests that the DBE can occur in several other analogous periodic waveguides. These structures can be potentially used to investigate unconventional gain schemes in traveling wave tubes or other kinds of distributed amplifiers, oscillators and novel pulse compressors.

We present a transmission line theory of exceptional points of degeneracy (EPD) in coupled-mode guiding structures, i.e., a theory that illustrates the characteristics of coupled electromagnetic modes under a special dispersion degeneracy condition, yet unexplored in the contest of gain and loss. We show that coupled transmission lines (CTLs) at radio frequencies having gain (active devices) and loss (e.g., material, radiation) balance exhibit EPDs. We demonstrate the concept of parity-time (PT)-symmetry in uniform CTLs that involve symmetric gain and loss and how this condition is associated with a second-order EPD. Furthermore, we also demonstrate that $\mathcal {PT}$-symmetry is not a necessary condition for realizing EPDs, and indeed, we show that EPD is also obtained with asymmetric distributions of gain and loss in uniform CTLs. We further propose potential applications of the EPDs in designing leaky-wave antennas with the capability of beam and directivity control as well as enhanced sensitivity. Operating near such special degeneracy conditions leads to potential performance enhancement in a variety of microwave and optical resonators, antennas, and devices such as distributed oscillators, including lasers, amplifiers, radiating oscillators, pulse compressors, and Q-switching sensors.

We introduce a graphene-based composite multilayer structure that exhibits hyperbolic-like wavevector dispersion at terahertz and mid-infrared frequencies. The multilayer structure comprises graphene sheets separated by dielectric layers. We formulate the effective permittivity tensor of the multilayer using a simple homogenization scheme. In addition, we employ Bloch theory for evaluating the wavevector dispersion for a propagation mode inside the HM, and show that the homogenization scheme is in good agreement with Bloch theory in a very wide spatial spectrum. We report the tunability of transition from elliptic to hyperbolic iso-frequency wavevector dispersion by varying the chemical potential of graphene sheets. © 2013 IEEE.

We demonstrate the existence of exceptional points of degeneracy (EPDs) of periodic eigenstates in non-Hermitian coupled chains of dipolar scatterers. Guided modes supported by these structures can exhibit an EPD in their dispersion diagram at which two or more Bloch eigenstates coalesce, in both their eigenvectors and eigenvalues. We show the emergence of a second-order modal EPD associated with the parity-time (PT) symmetry condition, at which each particle pair in the double chain exhibits balanced gain and loss. Furthermore, we also demonstrate a fourth-order EPD occurring at the band edge. Such a degeneracy condition was previously referred to as a degenerate band edge in lossless anisotropic photonic crystals. Here, we rigorously show it under the occurrence of gain and loss balance for a discrete guiding system. We identify a more general regime of gain and loss balance showing that PT symmetry is not necessary to attain EPDs. Moreover, we investigate the degree of detuning of the EPD when the geometrical symmetry or balanced condition is broken. Furthermore, we demonstrate a realistic implementation of the EPD in a coupled chain made of pairs of plasmonic nanospheres and active core-shell nanospheres at optical frequencies. These findings open avenues toward superior light localization and transport with application to high-Q resonators utilized in sensors, filters, low-threshold switching and lasing.

We investigate a novel implementation of hyperbolic metamaterial (HM) at far-infrared frequencies composed of stacked graphene sheets separated by thin dielectric layers. Using the surface conductivity model of graphene, we derive the homogenization formula for the multilayer structure by treating graphene sheets as lumped layers with complex admittances. Homogenization results and limits are investigated by comparison with a transfer matrix formulation for the HM constituent layers. We show that infrared iso-frequency wavevector dispersion characteristics of the proposed HM can be tuned by varying the chemical potential of the graphene sheets via electrostatic biasing. Accordingly, reflection and transmission properties for a film made of graphene-dielectric multilayer are tunable at terahertz frequencies, and we investigate the limits in using the homogenized model compared to the more accurate transfer matrix model. We also propose to use graphene-based HM as a super absorber for near-fields generated at its surface. The power emitted by a dipole near the surface of a graphene-based HM is increased dramatically (up to 5 × 10(2) at 2 THz), furthermore we show that most of the scattered power is directed into the HM. The validity and limits of the homogenized HM model are assessed also for near-fields and show that in certain conditions it overestimates the dipole radiated power into the HM.

We introduce graphene-based hyperbolic metamaterial for terahertz frequencies. The LDOS as well as the scattered power by a microsphere at its surface are enhanced by orders of magnitude, and controlled via chemical potential. © OSA 2013.

We investigated a multilayer graphene-dielectric composite material, comprising graphene sheets separated by subwavelength-thick dielectric spacer, and found it to exhibit hyperbolic isofrequency wavevector dispersion at far- and mid-infrared frequencies, allowing propagation of waves that would be otherwise evanescent in an isotropic dielectric. Electrostatic biasing was considered for tunable and controllable transition from hyperbolic to elliptic dispersion. We explored the validity and limitation of the effective medium approximation (EMA) for modeling wave propagation and cutoff of the propagating spatial spectrum due to the Brillouin zone edge. We reported that EMA is capable of predicting the transition of the isofrequency dispersion diagram under certain conditions. The graphene-based composite material allows propagation of backward waves under the hyperbolic dispersion regime and of forward waves under the elliptic regime. Transition from hyperbolic to elliptic dispersion regimes is governed by the transverse epsilon-near-zero (TENZ) condition, which implies a flatter and wider propagating spectrum with higher attenuation, when compared to the hyperbolic regime. We also investigated the wide-angle tunable transparency of the multilayer at that condition in contrast to other materials exhibiting ENZ phenomena. © 2013 Society of Photo-Optical Instrumentation Engineers.

We propose a new amplification regime based on a synchronous operation of four degenerate electromagnetic (EM) modes in a slow-wave structure and the electron beam, referred to as super synchronization. These four EM modes arise in a Fabry-Pérot cavity when degenerate band edge (DBE) condition is satisfied. The modes interact constructively with the electron beam resulting in superior amplification. In particular, much larger gains are achieved for smaller beam currents compared to conventional structures based on synchronization with only a single EM mode. We demonstrate giant gain scaling with respect to the length of the slow-wave structure compared to conventional Pierce type single mode traveling wave tube amplifiers. We construct a coupled transmission line model for a loaded waveguide slow-wave structure exhibiting a DBE, and investigate the phenomenon of giant gain via super synchronization using the Pierce model generalized to multimode interaction.

We propose a new principle of operation in vacuum electron-beam-based oscillators that leads to a low beam current for starting oscillations. The principle is based on supersynchronous operation of an electron beam interacting with four degenerate electromagnetic modes in a slow-wave structure (SWS). The four-mode supersynchronous regime is associated with a very special degeneracy condition in the dispersion diagram of a cold periodic SWS called degenerate band edge (DBE). This regime features a giant group delay in the finite-length SWS and low starting-oscillation beam current. The starting beam current is at least an order of magnitude smaller compared with a conventional backward-wave oscillator of the same length. As a representative example, we consider an SWS conceived by a periodically loaded metallic waveguide supporting a DBE and investigate starting-oscillation conditions using the Pierce theory generalized to coupled transmission lines. The proposed supersynchronism regime can be straightforwardly adapted to waveguide geometries others than the periodically loaded waveguide considered here since DBE is a general property that can be realized in a variety of structures.

A conventional periodic LC ladder circuit forms a transmission line that has a regular band edge between a passband and a stopband. Here for the first time, we develop the theory of simple yet unconventional double ladder circuit that exhibits a special degeneracy condition referred to as a degenerate band edge (DBE). The degeneracy occurs when four independent eigenstates coalesce into a single eigenstate at the DBE frequency. In addition to possible practical applications, this circuit may provide insight into DBE behavior that is not clear in more complex systems. We show that double ladder resonators exhibit unusual behavior of the loaded quality factor near the DBE, leading to a stable resonance frequency against load variations. These two properties in the proposed circuit are superior to the analogous properties in single ladder circuits. Our proposed analysis leads to analytic expressions for all circuit quantities thus providing insight into the very complex behavior near degeneracy points in periodic circuits. Interestingly, here we show for the first time That a DBE is obtained with unit cells that are symmetric along the propagation direction. The proposed theory of double ladders presented here has potential applications in filters, couplers, oscillators, and pulse shaping networks.